You are probably getting the Cathars, mixed up with the Templars, (a common error, yet odd, no apparent historical link.)
The Templars were not exterminated, their leaders were executed by the King of France. The others, disbanded by the Church, were sometimes ordered to do penance, but otherwise reassigned to different forms of religious life.
Many Templars didn't like this deal, and fled. A minority went as far as the Islamic world, where they lived on as advisors to Sultans. In Spain, although the order was supressed, the Church gave them pensions.
Good historical points, BlackVeil.
In Spain, where they built many churches, they were active in the protection of pilgrims, as were several other military orders. Most of the other military orders were also disbanded or passed into different forms over the years, but for some reason, partly because of their reputation for heterodoxy and the fact that some saw them as proto-Protestants, the Templars continued to feature in the literary imagination, particularly with "progressives," aka, leftists. I suspect the Masonic connection (Knights of DeMolay, etc) had something to do with that.
Now, of course, their churches are the object of "pilgrimages" by bunches of New Agers. I did the Camino de Santiago this fall, starting from Roncesvalles, and I found that more than one of my fellow pelegrinos was actually in search of Templar sites. I guess Gnosticism never quite goes away.